Sorry for the late reply. I have been on holiday for the last
two weeks.

What is the best workflow for automated testing?

It is a very broad question, and I'm afraid that I can't answer
it.

First of all, I don't know if there are any functional testing
tools specific for the combination of a mobile app + Starling +
Robotlegs 2 + Feathers. You can try your luck on a Starling forum,
or stackoverflow :)

There are general principles of functional testing, but the
concrete workflow is often dictated by the testing framework or a
combination of frameworks you decided to use.

TestComplete, RIATest, Ranorex are some good testing tools
(commercial).

FlexMonkey and Selenium-Flex are open source and free tools.

Not sure if the following resources are of any use to you, but
here they are anyway: